%0 Journal Article
%T Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Mahmoudieh, Mohammad
%A Hosseinnezhad, Hessam
%A Abbaspour Tabadkan, Gholamreza
%D 2019
%\ 07/01/2019
%V 15
%N 1
%P 1-18
%! Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules
%K Multi-frame vector
%K Wandering vector
%K Local commutant
%K Unitary system
%R 10.22130/scma.2018.77908.356
%X In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective operator is replaced by unitary and invertible operators, respectively. Moreover, we show that new multi-frames (resp. multi-Riesz bases) can be obtained as linear combinations of known ones using coefficients which are operators in a certain class.
%U https://scma.maragheh.ac.ir/article_34968_32b4b532a24202b9716e9e3469083a0a.pdf